An Electrostatic Storage Ring for Low Energy Electron Collisions

1
An Electrostatic Storage Ring for Low Energy
Electron Collisions
T J Reddish, D R Tessier, P Hammond, A J
Alderman, M R Sullivan, P A Thorn and F H
Read Department of Physics, University of
Windsor, Windsor, Canada N9B 3P4 School of
Physics, CAMSP, University of Western Australia,
Perth WA 6009, Australia School of Physics and
Astronomy, University of Manchester, Manchester
M13 9PL, UK
Introduction A racetrack shaped, desk-top sized
electrostatic storage ring has been developed
1. The apparatus is capable of storing any low
energy charged particle (i.e. electrons,
positrons, ions) and in the longer term, will be
used for ultra-high resolution electron
spectroscopy. We are currently investigating the
performance of the spectrometer using electrons
and hence refer to the system as an Electron
Recycling Spectrometer (ERS). We will shortly be
extending this design concept to ions.

• Specifications
• Orbital circumference of the storage ring is
  0.65m.
• Typical orbit time is 250ns 350ns for
  electrons, depending on energy.
• Electrons energies at the interaction region
  150 eV.
• Storage lifetimes of 50 ms have been observed,
  corresponding to 200 orbits.

Recycling The sharp peaks in the spectrum below
correspond primarily to fast electrons that have
elastically scattered from helium target gas. (A
background signal from metastable helium ions has
been removed form the spectrum.) Each peak
corresponds to a further orbit of the initial
injection pulse and clearly shows recycling
continuing for 48 ?s. Also highlighted in this
spectrum is the decaying amplitude of the
electron signal. The (x 200) insert shows the
recycling peaks uniformly decaying in amplitude
and characterized by a 13.6 ?s decay life-time.
1 Tessier et al., Phys. Rev. Lett., 99 253201,
2007.
Criteria For Stable Recycling
Below is a mosaic plot showing the logarithm of
ERS yield as a function of storage time and V2
for V3/V1 2. There are several regions of
stability, the strongest at V2 130 V
corresponding to the (H,m) (2,1) mode. The
other regions are also in good agreement with the
predictions, as shown. See 2 for more details.
Electrostatic thick lens. Focal lengths f1 and
f2 mid-focal lengths F1 and F2 position of
target and image P and Q, respectively. K1 P
F1 K2 Q F2.
2 Hammond et al. N. J. Phys. 11 043033, 2009.
Standard matrix methods are used to predict the
trajectories of charged particles within storage
rings.
Physically, this signifies both the overall
linear and angular magnifications are ? 1, and
therefore do not diverge with multiple orbits.
Mss can be determined as the product of the
transfer matrices for smaller sections of the
storage ring. Hence Mss MstMts, where Mst is
the transfer matrix for the source to target
section of the storage ring and Mts, that for the
target to source section. Under symmetric
operating conditions the potentials, V3, of the
source and interaction regions are equal.
Additionally the potentials of the top and
bottom hemispheres, V1, are the same and the
potentials, V2, are the same for all four lenses.
Therefore the ERS is symmetric in both reflection
planes A and B (see schematic diagram) and Mst is
equal to Mts. Mst m2mhm1, where m1, mh, and m2
are defined below.
The above figure shows the numerically computed
non-paraxial trajectory of an electron
undertaking multiple orbits of the ERS close to
the H 2 and m 1 condition. Although the
trajectory does not retrace itself after 2
orbits, which occurs when (2,1) is exactly
satisfied, it does still produce an overall time
averaged stable beam.
We now consider asymmetric operating conditions.
This is achieved by breaking the symmetry in
reflection plane A. To do this we set different
potentials on the lenses in the top (V2t) and
bottom (V2b) halves of the ERS and/or set
different pass energies to the top and bottom
hemispherical analysers. The left figure below
shows the predicted regions of stability for a
range of lens potentials, with V1t 9V, V1b
18V. The blue shaded areas in the figure are
regions of expected stability. The right figure
below is experimental data taken with the same
potentials as the theory on the left.
Lens 2 is physically the same as lens 1, but
traversed by the electrons in the opposite
direction.
In any real system the lens geometry is fixed and
the lens parameters f1, f2, K1, K2, defined in
the Figure above, are controlled by the applied
voltages.
where ? and L are real. Employing the two
expressions for Mss, as described in 2, results
in
(H,m) modes describe a trajectory that, if
paraxial, retraces itself every H/m orbits. In
2 we show that odd H, even m modes are unstable
due to angular aberrations in the hemispherical
analysers.
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